A unit of the above-described type is known from DE 32 30 455 C2. Body parts of two different motor vehicle models can be positioned and welded. The body parts are placed on an assembly frame, which is also called geometry skid in practice, and is brought into a welding station together with the assembly frame. Replaceable positioning means, with which the body parts lying on the assembly frame are positioned before they are welded together, are arranged in the area of the welding station. The assembly frame is then moved on with the welded body parts. However, this is not sufficient in modern production lines for motor vehicles if a frequent change from one model to another is required, e.g., between motor vehicles with four doors, with two doors or station wagons.